# Mathematics and Statistics (MMathStat) (Full-Time, 2021 Entry)

**UCAS Code**

GGC3

**Qualification**

Master of Mathematics and Statistics (MMathStat)

**Duration**

4 years full-time

**Start Date**

27 September 2021

**Department of Study**

Department of Statistics

**Location of Study**

University of Warwick

Mathematics enhances your ability to think clearly, learn new ideas quickly, manipulate precise and intricate concepts, follow complex reasoning, construct logical arguments and expose dubious ones. The demand for mathematical statisticians has expanded so rapidly in recent years that both within and outside the academic world there is a severe shortage of well-qualified people.

## Course overview

The demand for mathematical statisticians has expanded so rapidly in recent years that both within and outside the academic world there is a severe shortage of well-qualified people. These degrees enable you to specialise in both pure mathematics and statistics. They offer flexibility and a wide choice of options in Computing, Operational Research and all the other topics available to Mathematics students.

The BSc and MMathStat are the same for the first two years of study, making it easy to reconsider your preference in the second year. Differences become apparent in the final years, with the MMathStat degree offering a supervised research project and the possibility to specialise in areas such as advanced statistics, biostatistics, computational statistics, actuarial and financial mathematics, and probability.

### Course structure

You will learn through a combination of lectures, small-group tutorials and practical sessions based in the Department's well-equipped undergraduate computing laboratory. A central part of learning in Mathematics and Statistics is problem solving. We encourage and guide students in tackling a variety of theoretical exercises and computing tasks.

Core first and second-year modules covering probability, sets, mathematical statistics, linear algebra and modelling build a solid foundation of essential mathematical and statistical knowledge and skills. You’ll also have flexibility to choose some options. In your third year, you will select half of your modules from Statistics and half from further options available in Statistics, Mathematics and other selected Departments.

### How will I learn?

The curriculum is divided up into modules consisting of lectures and assessments, which are often supplemented by smaller group teaching such as tutorials, supervisions and computer labs.

Homework assignments are often biweekly and the expectation is that students work hard trying to tackle problems covering a range of levels of difficulty.

### Contact hours

Contact time is around 15 hours a week.

### Class size

Class sizes vary from 15 students for selected optional modules up to 350 students for some core modules. Support classes usually consist of 15 students.

### How will I be assessed?

You will be assessed by a combination of closed and open-book examinations, continuous assessment and project work, depending on your options. Your final year will include a significant project including a presentation, academic poster and dissertation. The first year counts 10%, the second year 20%, the third year 30% and the fourth year 40% towards the final integrated masters degree mark.

### Study abroad

We support student mobility through study abroad programmes and all students have the opportunity to apply for an intercalated year abroad at one of our partner universities. The Study Abroad Team based in the Office for Global Engagement offers support for these activities, and the Department's dedicated Study Abroad Co-ordinator can provide more specific information and assistance.

### Work experience

You may additionally choose to spend an ‘intercalated’ year in an approved industry, business or university between your last two years at Warwick.

### General entry requirements

#### A level:

- A*AA to include A* in Mathematics and A in Further Mathematics
**OR**AAA to include Mathematics + STEP (grade 2)

#### IB:

- 37 overall to include 7 in Higher Level Mathematics ‘Analysis and Approaches’
**OR**36 overall to include 6 in Higher Level Mathematics ‘Analysis and Approaches’ + STEP (grade 2)**OR**36 overall to include 7 in Higher Level Mathematics ‘Applications and Interpretations’ + STEP (grade 2)

**Alternative offers and additional requirements:**

Find out more about our typical conditional offers.

You will also need to meet our English Language requirements.

### International Students

We welcome applications from students with other internationally recognised qualifications.

Find out more about international entry requirements.

### Contextual data and differential offers

Warwick may make differential offers to students in a number of circumstances. These include students participating in the Realising Opportunities programme, or who meet two of the contextual data criteria. Differential offers will be one or two grades below Warwick’s standard offer (to a minimum of BBB).

### Warwick International Foundation Programme (IFP)

All students who successfully complete the Warwick IFP and apply to Warwick through UCAS will receive a guaranteed conditional offer for a related undergraduate programme (selected courses only).

Find out more about standard offers and conditions for the IFP.

### Taking a gap year

Applications for deferred entry welcomed.

### Interviews

We do not typically interview applicants. Offers are made based on your UCAS form which includes predicted and actual grades, your personal statement and school reference.

### Year One

###### Linear Algebra

Linear algebra addresses simultaneous linear equations. You will learn about the properties of vector space, linear mapping and its representation by a matrix. Applications include solving simultaneous linear equations, properties of vectors and matrices, properties of determinants and ways of calculating them. You will learn to define and calculate eigenvalues and eigenvectors of a linear map or matrix. You will have an understanding of matrices and vector spaces for later modules to build on.

###### Mathematical Analysis

Analysis is the rigorous study of calculus. In this module there will be considerable emphasis throughout on the need to argue with much greater precision and care than you had to at school. With the support of your fellow students, lecturers and other helpers, you will be encouraged to move on from the situation where the teacher shows you how to solve each kind of problem, to the point where you can develop your own methods for solving problems. By the end of the year you will be able to answer interesting questions like, what do we mean by `infinity'?

###### Sets and Numbers

It is in its proofs that the strength and richness of mathematics is to be found. University mathematics introduces progressively more abstract ideas and structures, and demands more in the way of proof, until most of your time is occupied with understanding proofs and creating your own. Learning to deal with abstraction and with proofs takes time. This module will bridge the gap between school and university mathematics, taking you from concrete techniques where the emphasis is on calculation, and gradually moving towards abstraction and proof.

###### Statistical Laboratory 1

If you’re studying ST115 (Introduction to Probability) or ST111/2 (Probability), this course supports your understanding of statistical analysis. You’ll lay foundations for applying mathematical probability, and learn to calculate using probabilities and expectations. You’ll become familiar with the R software package for exploratory data analysis, and gain experience of elementary simulation techniques on real data, and, using visualisations, be able to propose probabilistic models for simple data sets. You’ll also cover sampling technique (standard discrete and continuous distributions – Bernoulli, geometric, Poisson, Gaussian and gamma) and learn generic sampling methods for univariate distributions, preparing you to move on to ST221 (Linear Statistical Modelling).

###### Introduction to Probability

Following modules MA137 and MA138, this builds your knowledge by introducing key notions of probability and developing your ability to calculate using probabilities and expectations. You’ll experiment with random outcomes through the notion of events and their probability, and look at examples of discrete and continuous probability spaces. You’ll learn counting methods (inclusion–exclusion formula and binomial co-efficients), and study theoretical topics including conditional probability and Bayes’ Theorem. Later, you’ll scrutinise important families of distributions and the distribution of random variables, and the light this shines on the properties of expectations. Finally, you’ll examine mean, variance and co-variance of distribution, through Chebyshev's and Cauchy-Schwartz inequalities.

###### Mathematical Techniques

Want to think like a mathematician? This practical, problem-solving module is for you. Building on your A-level knowledge, you’ll develop a deeper understanding of mathematical concepts and relations, using problem-solving techniques such as visualisation and pattern exploration. Using concrete examples from counting, combinatorics, calculus, geometry and inequalities, you will learn to express mathematical concepts clearly and precisely and enhance your mathematical and logical reasoning and communication skills. By the end of the module, you’ll be able to comprehend, construct, visualise and present a coherent mathematical argument.

### Year Two

###### Metric Spaces

A metric space is any set provided with a sensible notion of the `distance’ between points. In this module, you will examine how concepts such as convergence of sequences, continuity of functions and completeness can be extended to general metric spaces. This enables you to prove some powerful and important results, used in many parts of mathematics. Describing continuity in terms of open subsets takes you to the more general context of a topological space, where, instead of a distance, it is declared which subsets are open. You will be able to work with continuous functions, and recognise whether spaces are connected, compact or complete.

**Mathematical Analysis III**

This module considers integration and the convergence of sequences and series of functions. The idea behind integration is to compute the area under a curve. This involves taking a limit, and the deeper properties of integration require a precise and careful analysis of this limiting process. In this module you will learn how to prove that every continuous function can be integrated, and the fundamental theorem of calculus which gives the precise relation between integration and differentiation. You will learn how integration can be applied to define some of the basic functions of analysis and to establish their fundamental properties. Furthermore, many functions can be written as limits of sequences of simpler functions (or as sums of series): thus a power series is a limit of polynomials, and a Fourier series is the sum of a trigonometric series with coefficients given by certain integrals. You will learn methods for deciding when a function defined as the limit of a sequence of other functions is continuous, differentiable, integrable, and for differentiating and integrating this limit.

###### Stochastic Processes

The concept of a stochastic (developing randomly over time) process is a useful and surprisingly beautiful mathematical tool in economics, biology, psychology and operations research. In studying the ideas governing sequential stochastic processes, you’ll learn about Markov chains, which use conditional probability for a widely applicable family of random processes; random walks – the building blocks for constructing other processes as well as being important in their own right – and renewal theory, for processes that ‘begin all over again’. Your understanding will extend to notions of behaviour, including transience, recurrence and equilibrium, and you will apply these ideas to problems in probability theory.

###### Mathematical Methods

Following the algebraic modules MA106 and MA137, you’ll gain expertise in the everyday techniques of probability and statistics essential to your continued study. You’ll gain a grounding in optimisation, convergence, regression and best approximation. By the end of your course, expect to apply multivariate calculus (integration, calculation of under-surface volumes, variable formulae and Fubini’s Theorem) and to use partial derivatives, critical points and extrema, and to understand constrained optimisation. You’ll work on eigenvalues and eigenvectors, diagonalisation, characteristic polynomials, constant co-efficient differential equations, and orthogonal bases and orthonormalisation. You’ll also study convergence and continuity in metric spaces to advance your mathematical thinking.

###### Mathematical Statistics Part A

If you have already completed ST115, on this module, you’ll have the opportunity to acquire the knowledge you need to study more advanced topics in probability. You’ll study discrete, continuous and multivariate distributions in greater depth, and also learn about Jacobian transformation formula, conditional and multivariate Gaussian distributions, and the related distributions Chi-squared, Student’s and Fisher. In the second part, you’ll move on to more advanced topics, including moment-generating functions for random variables, convergence, and the Law of Large Number and the Central Limit Theorem.

###### Mathematical Statistics Part B

If you’ve completed Part A, this second-term module is your next step, where you’ll study the major ideas behind statistical inference, with an emphasis on likelihood methods of estimation, repeated sampling, and testing. You’ll learn to apply important models (such as the parametrised statistical model), hypothesis tests, linear models, estimators, and the Chi-squared goodness of fit. You’ll spend time calculating sampling distributions (Fisher’s theorem), and confidence intervals, and understand the principles of data reduction, point estimation and the notion of sufficient statistics. You’ll also become familiar with asymptotic normality and contingency tables, giving you a very firm foundation for your future engagement in advanced mathematical statistics.

###### Linear Statistical Modelling

If you’re taking modules ST115 ST218 or ST219, you’ll benefit from the study of statistical modelling on this course. Starting with an introduction to R software, you’ll learn to use this for modelling, specifically linear models, in a variety of different scenarios. You’ll scrutinise simple linear regression and distributions of estimators and residuals, before moving to multiple and polynomial regression, and learning how the study of residuals can inform your choice of model. You’ll also become acquainted with various ANOVA models and how R software can code and interpret them. Finally, you’ll gain a basic understanding of linear models for time series and frequency data.

### Final Years

The third year of MMathStat includes compulsory modules on advanced probability and statistical modelling and many optional modules. Overall you must take at least five statistics modules and at least two mathematics modules. The fourth (final) year of MMathStat offers many options in statistics, mathematics and beyond, and you also choose a Master's level dissertation topic from a wide selection of areas in statistics.

#### Examples of optional modules/options for current students

- Differential Equations
- Introduction to Quantitative Economics
- Geometry and Motion
- Introduction to Abstract Algebra
- Games, Decisions and Behaviour
- Introduction to Mathematical Finance
- Professional Practice of Data Analysis
- Programming for Data Science

### Tuition fees

Find out more about fees and funding

### Additional course costs

There may be costs associated with other items or services such as academic texts, course notes, and trips associated with your course. Students who choose to complete a work placement will pay reduced tuition fees for their third year.

### Your career

Recent graduates have pursued job roles such as:

- Actuaries, economists and statisticians
- Software developers
- Chartered and certified accountants
- Finance and investment analysts
- Teachers
- Telecommunication designers
- Data scientists and engineers
- Academics

UK firms that have employed recent Warwick graduates from the Mathematics and Statistics Departments include:

- Adder Technology
- Amazon
- BlackRock International
- Merrill Lynch
- Brainlabs
- Civil Service
- Conduent
- Darktrace
- Deloitte
- Department of Health
- eBay
- Ford Motor Company
- Fore Consulting
- Goldman Sachs
- Government Actuaries
- Investec
- Jane Street Capital
- KPMG
- Lloyds
- MBDA
- Metaswitch
- Met Office
- Ministry of Justice
- RenaissanceRe (Syndicate 1458)
- Oxford Clinical Trials Unit
- Softwire
- Solid Solutions
- Sword Apak
- Ten10
- Towers Watson
- Xafinity

### Helping you find the right career

Our department has a dedicated professionally qualified Senior Careers Consultant to support you. They offer impartial advice and guidance, together with workshops and events throughout the year. Previous examples of workshops and events include:

- Finding experience to boost your CV in Year One and Two
- Careers in Data Science and Artificial Intelligence
- Warwick careers fairs throughout the year
- Interview skills for Statistics students
- Maths and Stats Careers Fair

"I feel like I get a lot of support here. I don't think I'd have access to the modules that I take here anywhere else, and I know that when I want to do research projects I can go up to a member of staff and ask for their help - I have received a lot of support for that.

We've just got a brand new building and it's gorgeous. It's made studying a lot easier as we've got a brand new computer suite and common room (and it means that people have been brought together a lot more in the department).

I've got a really great personal tutor, he's always there for me when I need to go talk to him. I've also got a really good supervisor, he's been really helpful at picking out topics for what to research into. The lecturers have been really great you can always go and ask them questions.”

CarmenBSc Mathematics and Statistics

This information is applicable for 2021 entry. Given the interval between the publication of courses and enrolment, some of the information may change. It is important to check our website before you apply. Please read our terms and conditions to find out more.